UV Unwrap model as multiple flat straight strips
Still some manual editing ............


Remove the outer edge seams so that those sides will be attached to the outer face UV islands when unwrapped.
Select those outer faces and sides and unwrap using the Conformal method.





Select only the inner faces and unwrap.
In the UV editor move these new UV islands to the right so that they will not be overlapping the outer faces UV's.





In the UV editor straighten out edges where necessary.




If you need to separate the sides UV's from the outer faces UV's.......


In the UV Editor, select two edges that make up one of the sides and hit the  Y  (to separate)  X  (to confine in the X axis)  G  to move and drag the new island away to clear space on the UV square.
Repeat for the other 3 sides.